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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 6: Q9. (page 207)

Complete the proof $m ∠ R O T > m ∠ S O V$ if given is $m ∠ R O S > m ∠ T O V$ .

Short Answer

Expert verified

Statement	Reason
$m ∠ R O S = m ∠ R O T - m ∠ S O T$	From the property of inequality.
$m ∠ R O S > m ∠ T O V$	Substitution property
$m ∠ R O T > m ∠ S O V$	Property of inequality.

If $m ∠ R O S > m ∠ T O V$ then by the use of the property of inequality $m ∠ R O T > m ∠ S O V$ .

Step by step solution

01

Step 1. Property of inequality

If $a > b$ and $c \geq d$ then $a + c > b + d$ .

02

Step 2. Show that angle addition postulate

From figure $m ∠ R O T = m ∠ R O S + m ∠ S O T$ and $m ∠ S O V = m ∠ T O V + m ∠ S O T$ .

03

– Prove that m M

Proof:

Since $m ∠ R O T = m ∠ R O S + m ∠ S O T$ and $m ∠ S O V = m ∠ T O V + m ∠ S O T$

$m ∠ R O S = m ∠ R O T - m ∠ S O T$	From the property of inequality.
$m ∠ R O S > m ∠ T O V$	Substitution property
$m ∠ R O T > m ∠ S O V$	Property of inequality.

Hence proved $m ∠ R O T > m ∠ S O V$ .

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